Question

A particular insulation material comes in 1 inch thick standard sheets. The material’s heat retention capacity is exponentially distributed with mean 1/c degrees Fahrenheit, where c is a fixed number (industry constant). Heat retention is additive in thickness and sheets added back to back act independently of each other for this insulation material. What is the mean and variance in heat retention capacity of back to back insulation of 5 standard sheets of this material?

Answer 1

Answer:

Given,

To give the mean and variance in heat retention capacity of back to back insulation of 5 standard sheets of this material

Let us consider x be exponentially distributed with a mean value of 1/c

Mean = 1/c

Overall retention = Y

= X + X + X + X + X

= 5X

Now,

E(Y) = 5*E(X)

substitute mean in E(Y)

E(Y) = 5*1/c

= 5/c

Now standard deviation for 1 sheet = 1/c [Here mean = standard deviation in exponential distribution]

Standard deviation(Y) = SD(5x)

= 5/c

So variance of Y = (5/c)^2

= 25/c^2

Variance of Y = 25/c^2